MAYBE
Time: 0.362

Problem:
 Equations:
  +AC(+AC(x4,x5),x6) -> +AC(x4,+AC(x5,x6))
  +AC(x4,x5) -> +AC(x5,x4)
  *AC(*AC(x4,x5),x6) -> *AC(x4,*AC(x5,x6))
  *AC(x4,x5) -> *AC(x5,x4)
  UAC(UAC(x4,x5),x6) -> UAC(x4,UAC(x5,x6))
  UAC(x4,x5) -> UAC(x5,x4)
  +AC(x4,+AC(x5,x6)) -> +AC(+AC(x4,x5),x6)
  +AC(x5,x4) -> +AC(x4,x5)
  *AC(x4,*AC(x5,x6)) -> *AC(*AC(x4,x5),x6)
  *AC(x5,x4) -> *AC(x4,x5)
  UAC(x4,UAC(x5,x6)) -> UAC(UAC(x4,x5),x6)
  UAC(x5,x4) -> UAC(x4,x5)
 TRS:
  0(#()) -> #()
  +AC(#(),x) -> x
  +AC(0(x),0(y)) -> 0(+AC(x,y))
  +AC(0(x),1(y)) -> 1(+AC(x,y))
  +AC(1(x),1(y)) -> 0(+AC(1(#()),+AC(x,y)))
  *AC(#(),x) -> #()
  *AC(0(x),y) -> 0(*AC(x,y))
  *AC(1(x),y) -> +AC(0(*AC(x,y)),y)
  *AC(+AC(y,z),x) -> +AC(*AC(x,y),*AC(x,z))
  UAC(empty(),b) -> b
  sum(empty()) -> 0(#())
  sum(singl(x)) -> x
  sum(UAC(x,y)) -> +AC(sum(x),sum(y))
  prod(empty()) -> 1(#())
  prod(singl(x)) -> x
  prod(UAC(x,y)) -> *AC(prod(x),prod(y))

Proof:
 Open